Building the yield curve in low-liquidity markets

Tsvetelin S Zaevski; Tsvetelin S Zaevski

doi:10.3934/DSFE.2026014

Data Science in Finance and Economics

2026, Volume 6, Issue 3: 397-424. doi: 10.3934/DSFE.2026014

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Building the yield curve in low-liquidity markets

Tsvetelin S Zaevski ^{1,2
,
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1.
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., Block 8, 1113 Sofia, Bulgaria
2.
Centre of Excellence in Informatics and Information and Communication Technologies, Sofia, Bulgaria

Received: 30 January 2026 Revised: 20 May 2026 Accepted: 31 May 2026 Published: 06 July 2026
JEL Codes: E43, E47, C02

This paper proposes a semi-statistical framework for constructing yield curves from primary-market government securities data in illiquid bond markets. Because government debt issuances are infrequent and sparse, the yield curve cannot be directly estimated from available market information. To address this limitation, the term structure of interest rates is characterized by classical affine stochastic models, calibrated through a transition-density-based estimation. For practical application, we employ the models of Vašíček and Cox–Ingersoll–Ross. The proposed framework combines historical observations with stochastic modeling to handle incomplete market data. The methodology is empirically evaluated using U.S. and Bulgarian Treasury securities. Results suggest that the approach produces stable and economically consistent yield curve estimates, particularly in environments where secondary-market data are limited or unreliable. The framework is especially relevant for emerging markets and may also support backtesting, forecasting, model validation, and structural analysis of bond markets.
- yield curve,
- term structure of interest rates,
- semi-statistical approach,
- Vašíček model,
- CIR model,
- American treasury securities
Citation: Tsvetelin S Zaevski. Building the yield curve in low-liquidity markets[J]. Data Science in Finance and Economics, 2026, 6(3): 397-424. doi: 10.3934/DSFE.2026014

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Abstract

This paper proposes a semi-statistical framework for constructing yield curves from primary-market government securities data in illiquid bond markets. Because government debt issuances are infrequent and sparse, the yield curve cannot be directly estimated from available market information. To address this limitation, the term structure of interest rates is characterized by classical affine stochastic models, calibrated through a transition-density-based estimation. For practical application, we employ the models of Vašíček and Cox–Ingersoll–Ross. The proposed framework combines historical observations with stochastic modeling to handle incomplete market data. The methodology is empirically evaluated using U.S. and Bulgarian Treasury securities. Results suggest that the approach produces stable and economically consistent yield curve estimates, particularly in environments where secondary-market data are limited or unreliable. The framework is especially relevant for emerging markets and may also support backtesting, forecasting, model validation, and structural analysis of bond markets.

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